In this paper, we present a new method for solving some certain differential systems in the artificial neural networks field. The analytic and approximate solutions are given with series form in the spaces W[a,b] and H[a,b]. The method used in this thesis has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, need less effort to achieve the results, an
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